An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications
Edición de la obra Geometry of Vector Sheaves
| Autor | Anastasios Mallios |
|---|---|
| Editorial | Springer Netherlands |
| Fecha de publicación | 1998 |
| Lugar | Dordrecht |
| Idioma | inglés |
| Páginas | 882 |
| Formato | [electronic resource] : |
| ISBN-13 | 9789401061025, 9789401150064 |
| ISBN-10 | 9401061025, 9401150060 |
| OCLC | 851375599 |
| Serie |
| Mathematics and Its Applications -- 439 · Mathematics and Its Applications -- 439 |
| Número de Cutter | M254g |
|---|
This two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth (CINFINITY) manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasised. This has theoretical advantages such as greater perspective, clarity and unification, but also practical benefits ranging from elementary particle physics, via gauge theories and theoretical cosmology (`differential spaces'), to non-linear PDEs (generalised functions). Thus, more general applications, which are no longer `smooth' in the classical sense, can be coped with. The treatise might also be construed as a new systematic endeavour to confront the ever-increasing notion that the `world around us is far from being smooth enough'. Audience: This work is intended for postgraduate students and researchers whose work involves differential geometry, global analysis, analysis on manifolds, algebraic topology, sheaf theory, cohomology, functional analysis or abstract harmonic analysis.